Hardware Reference
In-Depth Information
y
L
N'
I
V'
screen
(z=1)
z
S
y
S
x
V
x
N
Fig. 3.28
Simple 3D graphics benchmark
because exponents are in the higher halves, and the alignment shift is not necessary
if the higher halves are the same. Then the read operands are swapped if necessary
at the third and later steps. The alignment and addition are done at third to fifth
steps, and the lower and higher parts are outputted at fifth and last steps.
As a result, the FMUL, FADD, and FSUB take six steps. The conversion instruc-
tions of FLOAT, FTRC, FCNVSD, and FCNVDS take two steps mainly because a
double-precision operand requires two cycles to read or write.
3.1.5.3
Performance Evaluation with 3D Graphics Benchmark
The extended floating-point architecture was evaluated by a simple 3D graphics
benchmark shown in Fig.
3.28
. It consists of coordinate transformations, perspec-
tive transformations, and intensity calculations of a parallel beam of light in
Cartesian coordinates. A 3D-object surface is divided into triangular or quadrangu-
lar polygons to be treated by the 3D graphics. The benchmark uses triangular poly-
gons, and affine transformations, which consists of a rotation and a parallel
displacement. The perspective transformation assumes a flat screen expressed as
z
= 1. The benchmark is expressed as follows, where
A
represents an affine transfor-
mation matrix;
V
and
N
represent vertex and normal vectors of a triangle before the
coordinate transformations, respectively;
N
¢ and
V
¢ represent the ones after the
transformations, respectively;
S
and
S
represent
x
and
y
coordinates of the projec-
tion of
V
¢, respectively;
L
represents a vector of the parallel beam of light; and
I
represents an intensity of a triangle surface:
(
)
(
)
V
′
=
VSVVSVVN
,
=
′
/
′
,
=
′
/
′
,
′
=
NI
,
=
LN
,
′
/
NN
′
,
′
,
x
x
z
y
y
z
AAAA
⎛
⎞
V
⎛⎞
′
⎛⎞
V
xx
xy
xz
xw
x
x
⎜
⎟
⎜⎟
⎜⎟
AAAA
V
′
V
⎜
⎟
⎜⎟
yx
yy
yz
yw
⎜⎟
y
y
A
=
,
V
=
,
V
′
=
,
⎜
⎟
⎜⎟
⎜⎟
AAAA
V
V
′
zx
zy
zz
zw
z
⎜
⎟
z
⎜⎟
⎜
⎝⎠
1
⎝⎠
1
⎝
0001
⎠
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